Math

A square and an equilateral triangle have equal perimeters. The area of the triangle is
16�ã3 square centimeters, how long in centimeters is a diagonal of the square? Express your answer in simplest radical form.

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  1. let each side of the square be x cm
    let each side of the equilateral triangle be 2y cm (I use 2y to avoid fractions)

    so 4x = 6y,
    x = 3y/2

    using Pythagoras, the height of the triangle is (√3)y
    so
    (1/2)(2y)(√3)y = 16√3
    which solves to y = 4

    then x = 3(4)/2 = 6
    let the diagonal of the square be d
    d^2 = 6^2 + 6^2
    d = √72
    = 6√2

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